PINE LIBRARY
Mis à jour FunctionBaumWelch
Library "FunctionBaumWelch"
Baum-Welch Algorithm, also known as Forward-Backward Algorithm, uses the well known EM algorithm
to find the maximum likelihood estimate of the parameters of a hidden Markov model given a set of observed
feature vectors.
---
### Function List:
> `forward (array<float> pi, matrix<float> a, matrix<float> b, array<int> obs)`
> `forward (array<float> pi, matrix<float> a, matrix<float> b, array<int> obs, bool scaling)`
> `backward (matrix<float> a, matrix<float> b, array<int> obs)`
> `backward (matrix<float> a, matrix<float> b, array<int> obs, array<float> c)`
> `baumwelch (array<int> observations, int nstates)`
> `baumwelch (array<int> observations, array<float> pi, matrix<float> a, matrix<float> b)`
---
### Reference:
> en.wikipedia.org/wiki/Baum–Welch_algorithm
> github.com/alexsosn/MarslandMLAlgo/blob/4277b24db88c4cb70d6b249921c5d21bc8f86eb4/Ch16/HMM.py
> en.wikipedia.org/wiki/Forward_algorithm
> rdocumentation.org/packages/HMM/versions/1.0.1/topics/forward
> rdocumentation.org/packages/HMM/versions/1.0.1/topics/backward
forward(pi, a, b, obs)
Computes forward probabilities for state `X` up to observation at time `k`, is defined as the
probability of observing sequence of observations `e_1 ... e_k` and that the state at time `k` is `X`.
Parameters:
pi (float[]): Initial probabilities.
a (matrix<float>): Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing
states given a state matrix is size (M x M) where M is number of states.
b (matrix<float>): Emissions, matrix of observation probabilities b or beta = observation probabilities. Given
state matrix is size (M x O) where M is number of states and O is number of different
possible observations.
obs (int[]): List with actual state observation data.
Returns: - `matrix<float> _alpha`: Forward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first
dimension refers to the state and the second dimension to time.
forward(pi, a, b, obs, scaling)
Computes forward probabilities for state `X` up to observation at time `k`, is defined as the
probability of observing sequence of observations `e_1 ... e_k` and that the state at time `k` is `X`.
Parameters:
pi (float[]): Initial probabilities.
a (matrix<float>): Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing
states given a state matrix is size (M x M) where M is number of states.
b (matrix<float>): Emissions, matrix of observation probabilities b or beta = observation probabilities. Given
state matrix is size (M x O) where M is number of states and O is number of different
possible observations.
obs (int[]): List with actual state observation data.
scaling (bool): Normalize `alpha` scale.
Returns: - #### Tuple with:
> - `matrix<float> _alpha`: Forward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first
dimension refers to the state and the second dimension to time.
> - `array<float> _c`: Array with normalization scale.
backward(a, b, obs)
Computes backward probabilities for state `X` and observation at time `k`, is defined as the probability of observing the sequence of observations `e_k+1, ... , e_n` under the condition that the state at time `k` is `X`.
Parameters:
a (matrix<float>): Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing states
given a state matrix is size (M x M) where M is number of states
b (matrix<float>): Emissions, matrix of observation probabilities b or beta = observation probabilities. given state
matrix is size (M x O) where M is number of states and O is number of different possible observations
obs (int[]): Array with actual state observation data.
Returns: - `matrix<float> _beta`: Backward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first dimension refers to the state and the second dimension to time.
backward(a, b, obs, c)
Computes backward probabilities for state `X` and observation at time `k`, is defined as the probability of observing the sequence of observations `e_k+1, ... , e_n` under the condition that the state at time `k` is `X`.
Parameters:
a (matrix<float>): Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing states
given a state matrix is size (M x M) where M is number of states
b (matrix<float>): Emissions, matrix of observation probabilities b or beta = observation probabilities. given state
matrix is size (M x O) where M is number of states and O is number of different possible observations
obs (int[]): Array with actual state observation data.
c (float[]): Array with Normalization scaling coefficients.
Returns: - `matrix<float> _beta`: Backward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first dimension refers to the state and the second dimension to time.
baumwelch(observations, nstates)
**(Random Initialization)** Baum–Welch algorithm is a special case of the expectation–maximization algorithm used to find the
unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm
to compute the statistics for the expectation step.
Parameters:
observations (int[]): List of observed states.
nstates (int)
Returns: - #### Tuple with:
> - `array<float> _pi`: Initial probability distribution.
> - `matrix<float> _a`: Transition probability matrix.
> - `matrix<float> _b`: Emission probability matrix.
---
requires: `import RicardoSantos/WIPTensor/2 as Tensor`
baumwelch(observations, pi, a, b)
Baum–Welch algorithm is a special case of the expectation–maximization algorithm used to find the
unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm
to compute the statistics for the expectation step.
Parameters:
observations (int[]): List of observed states.
pi (float[]): Initial probaility distribution.
a (matrix<float>): Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing states
given a state matrix is size (M x M) where M is number of states
b (matrix<float>): Emissions, matrix of observation probabilities b or beta = observation probabilities. given state
matrix is size (M x O) where M is number of states and O is number of different possible observations
Returns: - #### Tuple with:
> - `array<float> _pi`: Initial probability distribution.
> - `matrix<float> _a`: Transition probability matrix.
> - `matrix<float> _b`: Emission probability matrix.
---
requires: `import RicardoSantos/WIPTensor/2 as Tensor`
Baum-Welch Algorithm, also known as Forward-Backward Algorithm, uses the well known EM algorithm
to find the maximum likelihood estimate of the parameters of a hidden Markov model given a set of observed
feature vectors.
---
### Function List:
> `forward (array<float> pi, matrix<float> a, matrix<float> b, array<int> obs)`
> `forward (array<float> pi, matrix<float> a, matrix<float> b, array<int> obs, bool scaling)`
> `backward (matrix<float> a, matrix<float> b, array<int> obs)`
> `backward (matrix<float> a, matrix<float> b, array<int> obs, array<float> c)`
> `baumwelch (array<int> observations, int nstates)`
> `baumwelch (array<int> observations, array<float> pi, matrix<float> a, matrix<float> b)`
---
### Reference:
> en.wikipedia.org/wiki/Baum–Welch_algorithm
> github.com/alexsosn/MarslandMLAlgo/blob/4277b24db88c4cb70d6b249921c5d21bc8f86eb4/Ch16/HMM.py
> en.wikipedia.org/wiki/Forward_algorithm
> rdocumentation.org/packages/HMM/versions/1.0.1/topics/forward
> rdocumentation.org/packages/HMM/versions/1.0.1/topics/backward
forward(pi, a, b, obs)
Computes forward probabilities for state `X` up to observation at time `k`, is defined as the
probability of observing sequence of observations `e_1 ... e_k` and that the state at time `k` is `X`.
Parameters:
pi (float[]): Initial probabilities.
a (matrix<float>): Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing
states given a state matrix is size (M x M) where M is number of states.
b (matrix<float>): Emissions, matrix of observation probabilities b or beta = observation probabilities. Given
state matrix is size (M x O) where M is number of states and O is number of different
possible observations.
obs (int[]): List with actual state observation data.
Returns: - `matrix<float> _alpha`: Forward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first
dimension refers to the state and the second dimension to time.
forward(pi, a, b, obs, scaling)
Computes forward probabilities for state `X` up to observation at time `k`, is defined as the
probability of observing sequence of observations `e_1 ... e_k` and that the state at time `k` is `X`.
Parameters:
pi (float[]): Initial probabilities.
a (matrix<float>): Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing
states given a state matrix is size (M x M) where M is number of states.
b (matrix<float>): Emissions, matrix of observation probabilities b or beta = observation probabilities. Given
state matrix is size (M x O) where M is number of states and O is number of different
possible observations.
obs (int[]): List with actual state observation data.
scaling (bool): Normalize `alpha` scale.
Returns: - #### Tuple with:
> - `matrix<float> _alpha`: Forward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first
dimension refers to the state and the second dimension to time.
> - `array<float> _c`: Array with normalization scale.
backward(a, b, obs)
Computes backward probabilities for state `X` and observation at time `k`, is defined as the probability of observing the sequence of observations `e_k+1, ... , e_n` under the condition that the state at time `k` is `X`.
Parameters:
a (matrix<float>): Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing states
given a state matrix is size (M x M) where M is number of states
b (matrix<float>): Emissions, matrix of observation probabilities b or beta = observation probabilities. given state
matrix is size (M x O) where M is number of states and O is number of different possible observations
obs (int[]): Array with actual state observation data.
Returns: - `matrix<float> _beta`: Backward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first dimension refers to the state and the second dimension to time.
backward(a, b, obs, c)
Computes backward probabilities for state `X` and observation at time `k`, is defined as the probability of observing the sequence of observations `e_k+1, ... , e_n` under the condition that the state at time `k` is `X`.
Parameters:
a (matrix<float>): Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing states
given a state matrix is size (M x M) where M is number of states
b (matrix<float>): Emissions, matrix of observation probabilities b or beta = observation probabilities. given state
matrix is size (M x O) where M is number of states and O is number of different possible observations
obs (int[]): Array with actual state observation data.
c (float[]): Array with Normalization scaling coefficients.
Returns: - `matrix<float> _beta`: Backward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first dimension refers to the state and the second dimension to time.
baumwelch(observations, nstates)
**(Random Initialization)** Baum–Welch algorithm is a special case of the expectation–maximization algorithm used to find the
unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm
to compute the statistics for the expectation step.
Parameters:
observations (int[]): List of observed states.
nstates (int)
Returns: - #### Tuple with:
> - `array<float> _pi`: Initial probability distribution.
> - `matrix<float> _a`: Transition probability matrix.
> - `matrix<float> _b`: Emission probability matrix.
---
requires: `import RicardoSantos/WIPTensor/2 as Tensor`
baumwelch(observations, pi, a, b)
Baum–Welch algorithm is a special case of the expectation–maximization algorithm used to find the
unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm
to compute the statistics for the expectation step.
Parameters:
observations (int[]): List of observed states.
pi (float[]): Initial probaility distribution.
a (matrix<float>): Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing states
given a state matrix is size (M x M) where M is number of states
b (matrix<float>): Emissions, matrix of observation probabilities b or beta = observation probabilities. given state
matrix is size (M x O) where M is number of states and O is number of different possible observations
Returns: - #### Tuple with:
> - `array<float> _pi`: Initial probability distribution.
> - `matrix<float> _a`: Transition probability matrix.
> - `matrix<float> _b`: Emission probability matrix.
---
requires: `import RicardoSantos/WIPTensor/2 as Tensor`
Notes de version
v2 minor update.Notes de version
Fix logger version.Notes de version
v4 - Added error checking for some errors.Notes de version
v5 - Improved calculation by merging some of the loops, where possible.Bibliothèque Pine
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Clause de non-responsabilité
Les informations et publications ne sont pas destinées à être, et ne constituent pas, des conseils ou recommandations financiers, d'investissement, de trading ou autres fournis ou approuvés par TradingView. Pour en savoir plus, consultez les Conditions d'utilisation.
Bibliothèque Pine
Dans l'esprit TradingView, l'auteur a publié ce code Pine sous forme de bibliothèque open source afin que d'autres programmeurs Pine de notre communauté puissent le réutiliser. Bravo à l'auteur! Vous pouvez utiliser cette bibliothèque à titre privé ou dans d'autres publications open source, mais la réutilisation de ce code dans des publications est régie par nos Règles.
Clause de non-responsabilité
Les informations et publications ne sont pas destinées à être, et ne constituent pas, des conseils ou recommandations financiers, d'investissement, de trading ou autres fournis ou approuvés par TradingView. Pour en savoir plus, consultez les Conditions d'utilisation.